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To solve for the **average rate of change** of the function \( f(x) \) between \( x = 3 \) and \( x = 7 \), we use the following formula:

\[
\text{Average Rate of Change} = \frac{f(7) - f(3)}{7 - 3}
\]

From the graph:
- The value of \( f(3) \) is approximately \( 1.5 \).
- The value of \( f(7) \) is approximately \( 5.5 \).

Substituting these into the formula:

\[
\text{Average Rate of Change} = \frac{5.5 - 1.5}{7 - 3} = \frac{4}{4} = 1
\]

So, the average rate of change is **1**.

Would you like any further clarification or more details on this? Here are a few related questions you could explore:

1. How would you find the instantaneous rate of change at \( x = 5 \)?
2. What does the sign of the average rate of change tell us about the function?
3. Could you estimate the average rate of change from \( x = 2 \) to \( x = 6 \)?
4. What would happen if \( f(7) \) was lower than \( f(3) \)? How would that affect the rate?
5. How can we calculate the slope between any two points on a graph?

**Tip:** The average rate of change is essentially the slope between two points on the graph, often interpreted as the "overall" trend of the function between those points.

Estimate the average rate of change from x = 3 to x = 7 based on the given graph of the function f(x).

Learn how to estimate the average rate of change of a function between x = 3 and x = 7 using the slope formula. This example uses a graph to approximate function values and calculate the rate of change. Suitable for students in Grades 8-10.

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